Quantum mechanics is weird. It has led respectable physicists to spin theories
about cats that are half alive and half dead, about worlds which split into
alternate universes with each quantum event, about a reality altered because an
intelligent observer watches it, about mathematical equations describing
"knowledge" rather than physical reality. This month's AV is about my
own work, a new interpretation of quantum mechanics which seeks to dispell this
weirdness by depicting each quantum event as a "transaction", a sort of
handshake across space-time. A long description of this
"Transactional
Interpretation" has just been published in the July Reviews of Modern
Physics (available at most university and major public libraries). It
challenges the standard Copenhagen Interpretation of Bohr and Heisenberg which
has maintained a shaky dominance as the orthodox interpretation of quantum
mechanics for over fifty years.

Quantum mechanics (QM) was invented in the late 1920's when an embarrassing
body of new experimental facts from the microscopic world couldn't be explained
by the accepted physics of the period. Heisenberg, Schroedinger, Dirac, and
others used a remarkable combination of intuition and brilliance to devise
clever ways of "getting the right answer" from a set of arcane mathematical
procedures. They somehow accomplished this without understanding in any basic
way what their mathematics really meant. The mathematical formalism of
quantum mechanics is now trusted by all physicists, its use clear and
unambiguous. But even now, five decades later, its meaning remains
controversial. One hears the platitude that "mathematics is the language of
science". Quantum mechanics reminds us that this "language" may lack a proper
translation, that formulating a theory is not the same as understanding its
meaning.

For orientation, let's start our discussion with some fairly simple questions
and answers:

Q: What is quantum mechanics?

A: It's the theory which deals with the smallest scale of physical
objects in the universe, objects (atoms, nuclei, photons, quarks) so small that
the lumpiness or quantization of physical variables becomes important.

Q: What is quantization?

A: Its the idea that there are minimum size chunks for certain
quantities like energy and angular momentum. The minimum energy chunk for
light of frequency f is E=hf where h is Planck's constant.
We call the particle of light carrying this minimum-size energy chunk hf
a photon.

Q: What is meant by "the formalism of quantum mechanics"?

A: Basically, the formalism is mathematics consisting of (1) a
differential equation like Schroedinger's wave equation which relates mass,
energy, and momentum; (2) the mathematical solutions of that wave equation,
called wave functions, which contain information about location, energy,
momentum, etc. of some system; and (3) procedures for using wave functions to
make predictions about physical measurements on the system.

Q: What's a "system"?

A: It is any collection of physical objects which is to be described by
quantum mechanics. It could be a single electron, a group of quarks, an atom,
a cat in a box, or the whole universe and all its contents.

Q: Why all the recent fuss about quantum mechanics?

A: Albert Einstein distrusted quantum mechanics because he perceived
embedded in its formalism what he called "spooky actions at a distance". The
characteristic which worried Einstein is called "nonlocality". The term
locality means that separated system parts which are out of
speed-of-light contact can only retain some definite relationship through
memory of previous contact. Nonlocality means that some relationship is
being enforced faster-than-light across space and time. The recent fuss has
arisen because the nonlocality of quantum mechanics has been spotlighted by the
EPR (Einstein-Podolsky-Rosen) experiments performed in the last decade. These
measurements of the correlated optical polarizations for oppositely directed
photons show that something very like faster-than-light hand-shaking must be
going on within the formalism of quantum mechanics and in nature itself.

Q: Finally, just what is the Copenhagen interpretation?

A: The Copenhagen interpretation of quantum mechanics is a set of ideas
and principles devised by Bohr, Heisenberg, and Born in the 1930's to give
meaning to the formalism of quantum mechanics and to avoid certain "paradoxes"
which seemed implicit in the formalism.

(1) Heisenberg's Uncertainty Principle, the idea that pairs of "conjugate"
variables (like position and momentum or energy and time) cannot simultaneously
be measured to "perfect" accuracy, nor can they have well-defined values at the
same time;

(2) Born's Probability Law, the rule that the absolute square of the wave
function gives the probability (P=|psi|2=psi×psi*) of finding
the system in the state described by the wave function;

(3) Bohr's Complementarity Principle, the idea that the uncertainty
principle is an intrinsic property of nature (not a just a measurement problem)
and that the observer, his measuring apparatus, and the measured system form a
"whole" which cannot be divided;

(4) Heisenberg's Knowledge Interpretation, the notion that the wave function
is neither a physical wave travelling through space nor a direct description of
a physical system, but rather is a mathematically encoded description of the
knowledge of an observer who is making a measurement on the
system; and

(5) Heisenberg's Positivism, the principle that it isn't proper to discuss
any aspect of the reality which lies behind the formalism unless the quantities
or entities discussed can be measured experimentally.

The first three elements of the Copenhagen interpretation are needed to
connect the formalism with the results of physical measurements. The last two
were devised by Heisenberg to deal with Einstein's "spooky actions at a
distance" criticism and similar problems which lie in the general area of
nonlocality. Let's consider an example of how the knowledge interpretation
handles nonlocality.

A excited atom gives up energy by spitting out a photon. The QM formalism
represents this event as a wave function which spreads out from the atom in an
ever-widening spherical wave front resembling the ring of ripples from a stone
thrown into a pond. The absolute square of this spreading wave function at a
particular point in space-time gives the probability of finding the photon
there. Finally the photon hits a silver atom in a photographic plate, giving
up its energy and leaving a black spot on the plate. Instantaneously the
photon's wave function undergoes a process called "collapse" which resembles
the pricking of a soap bubble. The wave function completely disappears from
all of space except in the immediate vicinity of the struck atom. The photon
has now delivered its energy to the silver atom and has no probability of
existing elsewhere. The wave function which had just been expanding through
time and space has abruptly vanished.

This vanishment is part of Einstein's "spookiness" criticism. In 1929 at a
physics conference he questioned how the remote parts of the wave function
could possibly know that it was time to vanish when the photon was detected.
Heisenberg's explanation was that the spreading wave function was not a real
wave moving through space at the speed of light but rather a representation of
the knowledge of an observer. When the observer had not yet detected the
photon, it has an equal probability of being anywhere on the spreading
spherical wave front. But as soon as the photon is detected it is know to have
travelled to the silver atom and its probability of being elsewhere must become
zero.

The problem with the knowledge interpretation comes when we try to stretch it
to the EPR experiments, a system of two polarization-correlated photons
travelling in opposite directions. Now there are two observers making
measurements and gaining information about two photons which are out of
speed-of-light contact, and yet the two measurements remain correlated in a
"spooky" way. The nonlocality which enforces this correlation cannot be
dismissed by attributing it to changes in knowledge. Something else must be
going on, and the Copenhageners can only retreat behind the shield of
Heisenberg's positivism in dealing with the problem.

The transactional interpretation meets the nonlocality problem
head on, using a "transaction" model for quantum events which is itself
nonlocal because it uses advancedwaves which have negative
energy and travel backwards in time. Advanced waves were the subject of a
previous AV column ["Light in Reverse Gear II",
August-1985 Analog]. This
transaction model is based on the "absorber theory" originated by Richard
Feynman and John Wheeler.

In the absorber theory description any emission process makes advanced waves on
an equal basis with ordinary "retarded" waves. But when the retarded wave is
absorbed (sometime in the future) a cancellation process takes place which
erases all traces of advanced waves and their "advanced" effects. The absorber
manages to absorb the retarded wave by making a second retarded wave identical
to but exactly out of phase with the retarded wave from the emitter. Thus the
two cancel and we say that the retarded wave from the emitter is absorbed.
However, the absorber also must make an advanced wave. This advanced wave
backtracks the retarded wave, travelling backwards in time along the path taken
by the retarded wave and reaching the emitter at the instant of
emission. It continues backward in time, but now it is accompanied by the
advanced wave from the emitter. The two waves are exactly out of phase, so
they also cancel, removing all "advanced" effects in the process.

An observer not privy to these inner mechanisms of nature would perceive only
that a retarded wave had gone from the emitter to the absorber. The absorber
theory description, unconventional though it is, leads to exactly the same
observations as the conventional one. But it differs in that there has been a
two-way exchange, a "handshake" across space-time which led to the transfer of
energy from emitter to absorber.

This advanced-retarded handshake is the basis for the transactional
interpretation of quantum mechanics. It is a two-way contract between the
future and the past for the purpose of transferring energy, momentum, etc. It
is nonlocal because the future is, in a limited way, affecting the past on the
same basis that the past affects the future. When you stand in the dark and
look at a star a hundred light years away, not only have the retarded light
waves from the star been travelling for a hundred years toward your eyes, but
also advanced waves from your eyes have reached a hundred years into the past
to encourage the star to shine in your direction. In my RMP paper this model
is used to explain the accumulation of curiosities and paradoxes (the EPR
paradox, Schroedinger's cat, Wigner's friend, Wheeler's delayed choice, etc.)
which have lain in the quantum mechanics Museum of Mysteries for decades. The
need for half-and-half cats, schizophrenic universes, observer-dependent
reality, or "knowledge" waves has been eliminated.

In this column we usually spotlight recent physics developments and then
consider their science fiction implications. The transactional interpretation
unfortunately pulls the rug from under a number of excellent SF works based on
the weirder aspects of quantum mechanics. Examples are Pohl's "The Coming of
the Quantum Cats" and Hogan's The Proteus Operation, both of which use
the many-worlds or Everett-Wheeler interpretation of quantum mechanics
[See
"The Alternate View: Other Universes II", November-1984 Analog]. The
transactional interpretation addressed the same problems which prompted
development the many-worlds interpretation and solves them in a more
satisfactory way.

There are SF possibilities in the transactional interpretation. Advanced waves
could perhaps, under the right circumstances, lead to "ansible-type" FTL
communication favored by LeGuin and Card and to backwards in time signaling of
the sort used in Benford's Timescape and Hogan's Thrice in Time.
There is also the implication implicit in the transactional interpretation that
Possibility does not become Reality along that sharp knife-edge that we call
"the present". Rather, Reality crystallizes along a much fuzzier boundary
which stitches into both future and past, advancing somehow in a way which
defies sharp temporal definition. There must be a story in that.